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*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 26 May 2012 12:22:50 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/26/t1338049449ct4ybc8blroc3yx.htm/, Retrieved Thu, 02 May 2024 21:16:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167620, Retrieved Thu, 02 May 2024 21:16:37 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2012-05-26 16:22:50] [012f495d97393010a2978331474c6aa8] [Current]

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Dataseries X:

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2,07
2,08
2,08
2,08
2,09
2,09
2,09
2,1
2,1
2,1
2,11
2,11
2,11
2,13
2,18
2,2
2,21
2,21
2,22
2,22
2,23
2,23
2,23
2,23
2,24
2,25
2,26
2,27
2,28
2,29
2,3
2,3
2,3
2,32
2,32
2,32
2,33
2,34
2,34
2,34
2,35
2,35
2,36
2,37
2,37
2,37
2,38
2,38
2,38
2,39
2,4
2,41
2,42
2,43
2,43
2,43
2,43
2,44
2,44
2,45

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167620&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167620&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167620&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0469378169412955
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0469378169412955 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167620&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0469378169412955[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167620&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167620&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0469378169412955
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	2.08	2.09	-0.0100000000000002
4	2.08	2.08953062183059	-0.00953062183058728
5	2.09	2.08908327524777	0.000916724752233478
6	2.09	2.09912630430637	-0.00912630430637229
7	2.09	2.09869793550549	-0.00869793550548925
8	2.1	2.09828967340097	0.00171032659903503
9	2.1	2.10836995239778	-0.00836995239778071
10	2.1	2.10797708510433	-0.00797708510432615
11	2.11	2.10760265814397	0.00239734185602547
12	2.11	2.11771518413716	-0.0077151841371581
13	2.11	2.11735305023646	-0.00735305023646005
14	2.13	2.1170079141105	0.0129920858894992
15	2.18	2.13761773425967	0.0423822657403328
16	2.2	2.18960706529055	0.0103929347094551
17	2.21	2.21009488695742	-9.48869574202149e-05
18	2.21	2.22009043317078	-0.0100904331707823
19	2.22	2.21961681026575	0.000383189734246336
20	2.22	2.22963479635535	-0.0096347963553538
21	2.23	2.22918256004776	0.000817439952240484
22	2.23	2.2392209288946	-0.00922092889459813
23	2.23	2.23878811862211	-0.00878811862211482
24	2.23	2.23837562351897	-0.00837562351897159
25	2.24	2.23798249003547	0.00201750996453143
26	2.25	2.24807718754886	0.00192281245113834
27	2.26	2.25816744016771	0.00183255983229458
28	2.27	2.26825345652565	0.00174654347435288
29	2.28	2.27833543546353	0.00166456453647301
30	2.29	2.28841356648903	0.00158643351097343
31	2.3	2.29848803021475	0.0015119697852457
32	2.3	2.30855899877575	-0.00855899877575483
33	2.3	2.30815725805802	-0.00815725805801781
34	2.32	2.30777437417255	0.0122256258274525
35	2.32	2.32834821835963	-0.00834821835962929
36	2.32	2.32795637121448	-0.00795637121447923
37	2.33	2.3275829165189	0.00241708348110325
38	2.34	2.33769636914086	0.0023036308591351
39	2.34	2.34780449654443	-0.00780449654443105
40	2.34	2.34743817051431	-0.00743817051430984
41	2.35	2.34708903902833	0.00291096097166932
42	2.35	2.35722567318154	-0.00722567318154255
43	2.36	2.35688651585647	0.00311348414353052
44	2.37	2.36703265600525	0.00296734399475218
45	2.37	2.37717193665448	-0.0071719366544758
46	2.37	2.37683530160467	-0.00683530160467338
47	2.38	2.37651446746921	0.00348553253078521
48	2.38	2.38667807075709	-0.00667807075708771
49	2.38	2.38636461669437	-0.00636461669437027
50	2.39	2.38606587548107	0.00393412451893171
51	2.4	2.39625053469756	0.00374946530243747
52	2.41	2.40642652641356	0.00357347358644411
53	2.42	2.4165942574626	0.003405742537399
54	2.43	2.42675411558237	0.00324588441762952
55	2.43	2.43690647031098	-0.00690647031097802
56	2.43	2.43658229567181	-0.0065822956718109
57	2.43	2.43627333708251	-0.00627333708251365
58	2.44	2.43597888033492	0.0040211196650759
59	2.44	2.44616762291366	-0.00616762291366202
60	2.45	2.44587812815838	0.00412187184162249

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.08 & 2.09 & -0.0100000000000002 \tabularnewline
4 & 2.08 & 2.08953062183059 & -0.00953062183058728 \tabularnewline
5 & 2.09 & 2.08908327524777 & 0.000916724752233478 \tabularnewline
6 & 2.09 & 2.09912630430637 & -0.00912630430637229 \tabularnewline
7 & 2.09 & 2.09869793550549 & -0.00869793550548925 \tabularnewline
8 & 2.1 & 2.09828967340097 & 0.00171032659903503 \tabularnewline
9 & 2.1 & 2.10836995239778 & -0.00836995239778071 \tabularnewline
10 & 2.1 & 2.10797708510433 & -0.00797708510432615 \tabularnewline
11 & 2.11 & 2.10760265814397 & 0.00239734185602547 \tabularnewline
12 & 2.11 & 2.11771518413716 & -0.0077151841371581 \tabularnewline
13 & 2.11 & 2.11735305023646 & -0.00735305023646005 \tabularnewline
14 & 2.13 & 2.1170079141105 & 0.0129920858894992 \tabularnewline
15 & 2.18 & 2.13761773425967 & 0.0423822657403328 \tabularnewline
16 & 2.2 & 2.18960706529055 & 0.0103929347094551 \tabularnewline
17 & 2.21 & 2.21009488695742 & -9.48869574202149e-05 \tabularnewline
18 & 2.21 & 2.22009043317078 & -0.0100904331707823 \tabularnewline
19 & 2.22 & 2.21961681026575 & 0.000383189734246336 \tabularnewline
20 & 2.22 & 2.22963479635535 & -0.0096347963553538 \tabularnewline
21 & 2.23 & 2.22918256004776 & 0.000817439952240484 \tabularnewline
22 & 2.23 & 2.2392209288946 & -0.00922092889459813 \tabularnewline
23 & 2.23 & 2.23878811862211 & -0.00878811862211482 \tabularnewline
24 & 2.23 & 2.23837562351897 & -0.00837562351897159 \tabularnewline
25 & 2.24 & 2.23798249003547 & 0.00201750996453143 \tabularnewline
26 & 2.25 & 2.24807718754886 & 0.00192281245113834 \tabularnewline
27 & 2.26 & 2.25816744016771 & 0.00183255983229458 \tabularnewline
28 & 2.27 & 2.26825345652565 & 0.00174654347435288 \tabularnewline
29 & 2.28 & 2.27833543546353 & 0.00166456453647301 \tabularnewline
30 & 2.29 & 2.28841356648903 & 0.00158643351097343 \tabularnewline
31 & 2.3 & 2.29848803021475 & 0.0015119697852457 \tabularnewline
32 & 2.3 & 2.30855899877575 & -0.00855899877575483 \tabularnewline
33 & 2.3 & 2.30815725805802 & -0.00815725805801781 \tabularnewline
34 & 2.32 & 2.30777437417255 & 0.0122256258274525 \tabularnewline
35 & 2.32 & 2.32834821835963 & -0.00834821835962929 \tabularnewline
36 & 2.32 & 2.32795637121448 & -0.00795637121447923 \tabularnewline
37 & 2.33 & 2.3275829165189 & 0.00241708348110325 \tabularnewline
38 & 2.34 & 2.33769636914086 & 0.0023036308591351 \tabularnewline
39 & 2.34 & 2.34780449654443 & -0.00780449654443105 \tabularnewline
40 & 2.34 & 2.34743817051431 & -0.00743817051430984 \tabularnewline
41 & 2.35 & 2.34708903902833 & 0.00291096097166932 \tabularnewline
42 & 2.35 & 2.35722567318154 & -0.00722567318154255 \tabularnewline
43 & 2.36 & 2.35688651585647 & 0.00311348414353052 \tabularnewline
44 & 2.37 & 2.36703265600525 & 0.00296734399475218 \tabularnewline
45 & 2.37 & 2.37717193665448 & -0.0071719366544758 \tabularnewline
46 & 2.37 & 2.37683530160467 & -0.00683530160467338 \tabularnewline
47 & 2.38 & 2.37651446746921 & 0.00348553253078521 \tabularnewline
48 & 2.38 & 2.38667807075709 & -0.00667807075708771 \tabularnewline
49 & 2.38 & 2.38636461669437 & -0.00636461669437027 \tabularnewline
50 & 2.39 & 2.38606587548107 & 0.00393412451893171 \tabularnewline
51 & 2.4 & 2.39625053469756 & 0.00374946530243747 \tabularnewline
52 & 2.41 & 2.40642652641356 & 0.00357347358644411 \tabularnewline
53 & 2.42 & 2.4165942574626 & 0.003405742537399 \tabularnewline
54 & 2.43 & 2.42675411558237 & 0.00324588441762952 \tabularnewline
55 & 2.43 & 2.43690647031098 & -0.00690647031097802 \tabularnewline
56 & 2.43 & 2.43658229567181 & -0.0065822956718109 \tabularnewline
57 & 2.43 & 2.43627333708251 & -0.00627333708251365 \tabularnewline
58 & 2.44 & 2.43597888033492 & 0.0040211196650759 \tabularnewline
59 & 2.44 & 2.44616762291366 & -0.00616762291366202 \tabularnewline
60 & 2.45 & 2.44587812815838 & 0.00412187184162249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167620&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]2.08[/C][C]2.09[/C][C]-0.0100000000000002[/C][/ROW]
[ROW][C]4[/C][C]2.08[/C][C]2.08953062183059[/C][C]-0.00953062183058728[/C][/ROW]
[ROW][C]5[/C][C]2.09[/C][C]2.08908327524777[/C][C]0.000916724752233478[/C][/ROW]
[ROW][C]6[/C][C]2.09[/C][C]2.09912630430637[/C][C]-0.00912630430637229[/C][/ROW]
[ROW][C]7[/C][C]2.09[/C][C]2.09869793550549[/C][C]-0.00869793550548925[/C][/ROW]
[ROW][C]8[/C][C]2.1[/C][C]2.09828967340097[/C][C]0.00171032659903503[/C][/ROW]
[ROW][C]9[/C][C]2.1[/C][C]2.10836995239778[/C][C]-0.00836995239778071[/C][/ROW]
[ROW][C]10[/C][C]2.1[/C][C]2.10797708510433[/C][C]-0.00797708510432615[/C][/ROW]
[ROW][C]11[/C][C]2.11[/C][C]2.10760265814397[/C][C]0.00239734185602547[/C][/ROW]
[ROW][C]12[/C][C]2.11[/C][C]2.11771518413716[/C][C]-0.0077151841371581[/C][/ROW]
[ROW][C]13[/C][C]2.11[/C][C]2.11735305023646[/C][C]-0.00735305023646005[/C][/ROW]
[ROW][C]14[/C][C]2.13[/C][C]2.1170079141105[/C][C]0.0129920858894992[/C][/ROW]
[ROW][C]15[/C][C]2.18[/C][C]2.13761773425967[/C][C]0.0423822657403328[/C][/ROW]
[ROW][C]16[/C][C]2.2[/C][C]2.18960706529055[/C][C]0.0103929347094551[/C][/ROW]
[ROW][C]17[/C][C]2.21[/C][C]2.21009488695742[/C][C]-9.48869574202149e-05[/C][/ROW]
[ROW][C]18[/C][C]2.21[/C][C]2.22009043317078[/C][C]-0.0100904331707823[/C][/ROW]
[ROW][C]19[/C][C]2.22[/C][C]2.21961681026575[/C][C]0.000383189734246336[/C][/ROW]
[ROW][C]20[/C][C]2.22[/C][C]2.22963479635535[/C][C]-0.0096347963553538[/C][/ROW]
[ROW][C]21[/C][C]2.23[/C][C]2.22918256004776[/C][C]0.000817439952240484[/C][/ROW]
[ROW][C]22[/C][C]2.23[/C][C]2.2392209288946[/C][C]-0.00922092889459813[/C][/ROW]
[ROW][C]23[/C][C]2.23[/C][C]2.23878811862211[/C][C]-0.00878811862211482[/C][/ROW]
[ROW][C]24[/C][C]2.23[/C][C]2.23837562351897[/C][C]-0.00837562351897159[/C][/ROW]
[ROW][C]25[/C][C]2.24[/C][C]2.23798249003547[/C][C]0.00201750996453143[/C][/ROW]
[ROW][C]26[/C][C]2.25[/C][C]2.24807718754886[/C][C]0.00192281245113834[/C][/ROW]
[ROW][C]27[/C][C]2.26[/C][C]2.25816744016771[/C][C]0.00183255983229458[/C][/ROW]
[ROW][C]28[/C][C]2.27[/C][C]2.26825345652565[/C][C]0.00174654347435288[/C][/ROW]
[ROW][C]29[/C][C]2.28[/C][C]2.27833543546353[/C][C]0.00166456453647301[/C][/ROW]
[ROW][C]30[/C][C]2.29[/C][C]2.28841356648903[/C][C]0.00158643351097343[/C][/ROW]
[ROW][C]31[/C][C]2.3[/C][C]2.29848803021475[/C][C]0.0015119697852457[/C][/ROW]
[ROW][C]32[/C][C]2.3[/C][C]2.30855899877575[/C][C]-0.00855899877575483[/C][/ROW]
[ROW][C]33[/C][C]2.3[/C][C]2.30815725805802[/C][C]-0.00815725805801781[/C][/ROW]
[ROW][C]34[/C][C]2.32[/C][C]2.30777437417255[/C][C]0.0122256258274525[/C][/ROW]
[ROW][C]35[/C][C]2.32[/C][C]2.32834821835963[/C][C]-0.00834821835962929[/C][/ROW]
[ROW][C]36[/C][C]2.32[/C][C]2.32795637121448[/C][C]-0.00795637121447923[/C][/ROW]
[ROW][C]37[/C][C]2.33[/C][C]2.3275829165189[/C][C]0.00241708348110325[/C][/ROW]
[ROW][C]38[/C][C]2.34[/C][C]2.33769636914086[/C][C]0.0023036308591351[/C][/ROW]
[ROW][C]39[/C][C]2.34[/C][C]2.34780449654443[/C][C]-0.00780449654443105[/C][/ROW]
[ROW][C]40[/C][C]2.34[/C][C]2.34743817051431[/C][C]-0.00743817051430984[/C][/ROW]
[ROW][C]41[/C][C]2.35[/C][C]2.34708903902833[/C][C]0.00291096097166932[/C][/ROW]
[ROW][C]42[/C][C]2.35[/C][C]2.35722567318154[/C][C]-0.00722567318154255[/C][/ROW]
[ROW][C]43[/C][C]2.36[/C][C]2.35688651585647[/C][C]0.00311348414353052[/C][/ROW]
[ROW][C]44[/C][C]2.37[/C][C]2.36703265600525[/C][C]0.00296734399475218[/C][/ROW]
[ROW][C]45[/C][C]2.37[/C][C]2.37717193665448[/C][C]-0.0071719366544758[/C][/ROW]
[ROW][C]46[/C][C]2.37[/C][C]2.37683530160467[/C][C]-0.00683530160467338[/C][/ROW]
[ROW][C]47[/C][C]2.38[/C][C]2.37651446746921[/C][C]0.00348553253078521[/C][/ROW]
[ROW][C]48[/C][C]2.38[/C][C]2.38667807075709[/C][C]-0.00667807075708771[/C][/ROW]
[ROW][C]49[/C][C]2.38[/C][C]2.38636461669437[/C][C]-0.00636461669437027[/C][/ROW]
[ROW][C]50[/C][C]2.39[/C][C]2.38606587548107[/C][C]0.00393412451893171[/C][/ROW]
[ROW][C]51[/C][C]2.4[/C][C]2.39625053469756[/C][C]0.00374946530243747[/C][/ROW]
[ROW][C]52[/C][C]2.41[/C][C]2.40642652641356[/C][C]0.00357347358644411[/C][/ROW]
[ROW][C]53[/C][C]2.42[/C][C]2.4165942574626[/C][C]0.003405742537399[/C][/ROW]
[ROW][C]54[/C][C]2.43[/C][C]2.42675411558237[/C][C]0.00324588441762952[/C][/ROW]
[ROW][C]55[/C][C]2.43[/C][C]2.43690647031098[/C][C]-0.00690647031097802[/C][/ROW]
[ROW][C]56[/C][C]2.43[/C][C]2.43658229567181[/C][C]-0.0065822956718109[/C][/ROW]
[ROW][C]57[/C][C]2.43[/C][C]2.43627333708251[/C][C]-0.00627333708251365[/C][/ROW]
[ROW][C]58[/C][C]2.44[/C][C]2.43597888033492[/C][C]0.0040211196650759[/C][/ROW]
[ROW][C]59[/C][C]2.44[/C][C]2.44616762291366[/C][C]-0.00616762291366202[/C][/ROW]
[ROW][C]60[/C][C]2.45[/C][C]2.44587812815838[/C][C]0.00412187184162249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167620&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167620&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	2.08	2.09	-0.0100000000000002
4	2.08	2.08953062183059	-0.00953062183058728
5	2.09	2.08908327524777	0.000916724752233478
6	2.09	2.09912630430637	-0.00912630430637229
7	2.09	2.09869793550549	-0.00869793550548925
8	2.1	2.09828967340097	0.00171032659903503
9	2.1	2.10836995239778	-0.00836995239778071
10	2.1	2.10797708510433	-0.00797708510432615
11	2.11	2.10760265814397	0.00239734185602547
12	2.11	2.11771518413716	-0.0077151841371581
13	2.11	2.11735305023646	-0.00735305023646005
14	2.13	2.1170079141105	0.0129920858894992
15	2.18	2.13761773425967	0.0423822657403328
16	2.2	2.18960706529055	0.0103929347094551
17	2.21	2.21009488695742	-9.48869574202149e-05
18	2.21	2.22009043317078	-0.0100904331707823
19	2.22	2.21961681026575	0.000383189734246336
20	2.22	2.22963479635535	-0.0096347963553538
21	2.23	2.22918256004776	0.000817439952240484
22	2.23	2.2392209288946	-0.00922092889459813
23	2.23	2.23878811862211	-0.00878811862211482
24	2.23	2.23837562351897	-0.00837562351897159
25	2.24	2.23798249003547	0.00201750996453143
26	2.25	2.24807718754886	0.00192281245113834
27	2.26	2.25816744016771	0.00183255983229458
28	2.27	2.26825345652565	0.00174654347435288
29	2.28	2.27833543546353	0.00166456453647301
30	2.29	2.28841356648903	0.00158643351097343
31	2.3	2.29848803021475	0.0015119697852457
32	2.3	2.30855899877575	-0.00855899877575483
33	2.3	2.30815725805802	-0.00815725805801781
34	2.32	2.30777437417255	0.0122256258274525
35	2.32	2.32834821835963	-0.00834821835962929
36	2.32	2.32795637121448	-0.00795637121447923
37	2.33	2.3275829165189	0.00241708348110325
38	2.34	2.33769636914086	0.0023036308591351
39	2.34	2.34780449654443	-0.00780449654443105
40	2.34	2.34743817051431	-0.00743817051430984
41	2.35	2.34708903902833	0.00291096097166932
42	2.35	2.35722567318154	-0.00722567318154255
43	2.36	2.35688651585647	0.00311348414353052
44	2.37	2.36703265600525	0.00296734399475218
45	2.37	2.37717193665448	-0.0071719366544758
46	2.37	2.37683530160467	-0.00683530160467338
47	2.38	2.37651446746921	0.00348553253078521
48	2.38	2.38667807075709	-0.00667807075708771
49	2.38	2.38636461669437	-0.00636461669437027
50	2.39	2.38606587548107	0.00393412451893171
51	2.4	2.39625053469756	0.00374946530243747
52	2.41	2.40642652641356	0.00357347358644411
53	2.42	2.4165942574626	0.003405742537399
54	2.43	2.42675411558237	0.00324588441762952
55	2.43	2.43690647031098	-0.00690647031097802
56	2.43	2.43658229567181	-0.0065822956718109
57	2.43	2.43627333708251	-0.00627333708251365
58	2.44	2.43597888033492	0.0040211196650759
59	2.44	2.44616762291366	-0.00616762291366202
60	2.45	2.44587812815838	0.00412187184162249

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	2.45607159982434	2.4394513895116	2.47269181013707
62	2.46214319964867	2.43808072346327	2.48620567583407
63	2.46821479947301	2.43805636332055	2.49837323562546
64	2.47428639929734	2.43866289459936	2.50990990399532
65	2.48035799912168	2.4396305099927	2.52108548825065
66	2.48642959894601	2.44082443163272	2.53203476625931
67	2.49250119877035	2.44216671759792	2.54283567994277
68	2.49857279859468	2.44360797655746	2.5535376206319
69	2.50464439841902	2.44511488096009	2.56417391587794
70	2.51071599824335	2.44666389039368	2.57476810609303
71	2.51678759806769	2.44823779108017	2.58533740505521
72	2.52285919789202	2.44982365061418	2.59589474516987

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 2.45607159982434 & 2.4394513895116 & 2.47269181013707 \tabularnewline
62 & 2.46214319964867 & 2.43808072346327 & 2.48620567583407 \tabularnewline
63 & 2.46821479947301 & 2.43805636332055 & 2.49837323562546 \tabularnewline
64 & 2.47428639929734 & 2.43866289459936 & 2.50990990399532 \tabularnewline
65 & 2.48035799912168 & 2.4396305099927 & 2.52108548825065 \tabularnewline
66 & 2.48642959894601 & 2.44082443163272 & 2.53203476625931 \tabularnewline
67 & 2.49250119877035 & 2.44216671759792 & 2.54283567994277 \tabularnewline
68 & 2.49857279859468 & 2.44360797655746 & 2.5535376206319 \tabularnewline
69 & 2.50464439841902 & 2.44511488096009 & 2.56417391587794 \tabularnewline
70 & 2.51071599824335 & 2.44666389039368 & 2.57476810609303 \tabularnewline
71 & 2.51678759806769 & 2.44823779108017 & 2.58533740505521 \tabularnewline
72 & 2.52285919789202 & 2.44982365061418 & 2.59589474516987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167620&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]2.45607159982434[/C][C]2.4394513895116[/C][C]2.47269181013707[/C][/ROW]
[ROW][C]62[/C][C]2.46214319964867[/C][C]2.43808072346327[/C][C]2.48620567583407[/C][/ROW]
[ROW][C]63[/C][C]2.46821479947301[/C][C]2.43805636332055[/C][C]2.49837323562546[/C][/ROW]
[ROW][C]64[/C][C]2.47428639929734[/C][C]2.43866289459936[/C][C]2.50990990399532[/C][/ROW]
[ROW][C]65[/C][C]2.48035799912168[/C][C]2.4396305099927[/C][C]2.52108548825065[/C][/ROW]
[ROW][C]66[/C][C]2.48642959894601[/C][C]2.44082443163272[/C][C]2.53203476625931[/C][/ROW]
[ROW][C]67[/C][C]2.49250119877035[/C][C]2.44216671759792[/C][C]2.54283567994277[/C][/ROW]
[ROW][C]68[/C][C]2.49857279859468[/C][C]2.44360797655746[/C][C]2.5535376206319[/C][/ROW]
[ROW][C]69[/C][C]2.50464439841902[/C][C]2.44511488096009[/C][C]2.56417391587794[/C][/ROW]
[ROW][C]70[/C][C]2.51071599824335[/C][C]2.44666389039368[/C][C]2.57476810609303[/C][/ROW]
[ROW][C]71[/C][C]2.51678759806769[/C][C]2.44823779108017[/C][C]2.58533740505521[/C][/ROW]
[ROW][C]72[/C][C]2.52285919789202[/C][C]2.44982365061418[/C][C]2.59589474516987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167620&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167620&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
61	2.45607159982434	2.4394513895116	2.47269181013707
62	2.46214319964867	2.43808072346327	2.48620567583407
63	2.46821479947301	2.43805636332055	2.49837323562546
64	2.47428639929734	2.43866289459936	2.50990990399532
65	2.48035799912168	2.4396305099927	2.52108548825065
66	2.48642959894601	2.44082443163272	2.53203476625931
67	2.49250119877035	2.44216671759792	2.54283567994277
68	2.49857279859468	2.44360797655746	2.5535376206319
69	2.50464439841902	2.44511488096009	2.56417391587794
70	2.51071599824335	2.44666389039368	2.57476810609303
71	2.51678759806769	2.44823779108017	2.58533740505521
72	2.52285919789202	2.44982365061418	2.59589474516987

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code